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Results tagged with pr.probability
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user 156792
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
3
votes
1
answer
801
views
Concentration inequality for the sample covariance matrix
I'd like to know if there is a concentration inequality for the sample covariance matrix that don't assume the knowledge of the true mean.
Background.
Given a probability distribution $\mu$ on $\math …
- 903
3
votes
Accepted
Concentration inequality for the sample covariance matrix
A variant of this (taking $\frac1m$ instead of $\frac1{m-1}$ for the empirical covariance) is answered on Proposition 2.6, page 10 of https://arxiv.org/pdf/2110.06357.pdf .
- 903
2
votes
1
answer
146
views
Tightly placed sphere caps
Problem. Fix a positive real $r>0$ and a positive integer $n>0$. Consider an independent, identical sample $X_1, \ldots X_n$ drawn from the uniform distribution over the unit $d$-sphere $\mathbb S^d \ …
- 903